Research Projects

Since my studies, I am fascinated by simulation and computing algorithms inspired by nature. Be it ant colony optimization for fleet routing, be it genetic algorithms for optimizing high dimensional paramterization problems, with my research company Green-ORCA I can tackle it.

The two-process model of Daan et. al (1984) was combined with a phase shifting and amplitude altering routine for better entrainment of the circadian processes by light. Genetic algorithms were used to find the appropriate model parameters for the natural distribution of different chronotypes (early birds, owls) that was published by Roenneberg (2007). As a breakthrough, the resulting distribution of one of the 8 free parameters - the circadian period - closely matched both distribution and average of the human circadian period published for experimantal data by Czeisler (1999).

I am thankful for the oportunity to give two lectures on Natural Optimization strategies at the University of Applied Science in Schmalkalden. The different ways of natural optimization provide powerful and fascinating opportunities to tackle mathematical problems beyond classic computational borders.

An ongoing project that has already been the core of my Diploma thesis:

In Collaboration with the Neuroinformatic Research Group at the University of Applied Science in Schmalkalden, a mathematical model for human Sleep-Wake-Rhythm prediction is proposed, that accounts for both Sleep homoeostatis and adaption of the circadian day to daylight.

The model shown above is a combination of the 2 Process Model [Daan,Beersma,Borbely] and the Phase Response Curve [DeCoursey, Pittendrigh]. The 2 Process Model (2PM) consists of the upper and lower sinodial circadian thresholds for sleep onset (green) and waketime (blue), further called Process C. In between, the sleep pressure (S) raises during waketime and falls during sleep. If one of the thresholds of Process C is met, S changes from Sleep to Wake state or vice versa.

The Phase Response Curve (PRC, thin blue line) is a mathematical model that accounts for the adaptation of the inner circadian clock to the solar day. Based on various experiments it was verified, that bright light in the subjective morning would accelerate the circadian clock, and bright light in the subjective evening slows it. Habitual sleeptime at night prevents the circadian clock to be altered too much. In the proposed combined model, both Process C and PRC run at the same circadian period (23.5 to 25hrs). If light hits an active part of the PRC, the phase shift is applied instantly to Process C and accumulated to later shifting on PRC. Further, the total sum of absolute product of light and PRC value during the day is calculated for attenuation of both PRC and Process C.

Humans happen the have different Sleep-Wake behaviours (further called Chronotypes), ranging from "Larks" awaking before sunrise after only 4.5hrs of sleep to "Owls" awaking just before noon after perhaps 12hrs of sleep. Various model parameters must be fitted to account for people with different chronotypes, which was achieved using Genetic Algorithms. The illustration below shows the fitting of a simulated Sleep-Wake-Cycle with fitted model parameters to the Sleep-Wake-Cycle recorded in a sleep diary over almost 150 days.

Based on our Sleep-Wake Model, shift schedules can be simulated for different chronotypes and examined for their suitability regarding sleep deprivation, forced waking and accumulated sleep lacks. Goal is to find schedules with reduced impact on these factors, hence provide better vigilance during work hours.

Scheduling hours and staff per crew are optimized with Genetic Algorithms to meet daily and hourly changing work demands in a 24/7 operation as displayed in the illustration below.

Goal is to reduce both Under- and Over staffing at any time during the week, and thereby improve both response times of the staff and overall performance. Further, schedules must meet legal and chronotypical requirements, that is schedules must contain appropriate rest phases and rotation patterns.

The next figure illustrates the optimisation of mis-scheduled working hours with GA during the optimization generations:

Many nowadays biofuel powerplants suffer inefficiency in several ways. The built-in electrical equipment is not commonly controlled by inverters but contactors. This results in both fast mechanical wearing of the mechanical components and power waste for full speed operation of the engines.

For a biofuel powerplant in Bavaria, possibilities to reduce both energy consumption and mechanical decay were analyzed. The suggested solution of implementing PLC driven and sensor controlled inverters for the electric ventilators, pumps and mixing equipment reduces the self power consumation from average 20kWh down to 10kWh per operating hour. For the estimated 200 annual operation days, savings of approximately 10T € can be achieved. With these savings, the initial costs for the inverters and sensors will be accumulated in approximately 1 year. In addition, mechanical wearing and maintenance downtime is greatly reduced.

Automatic fine-grain control of the input gas pressure for the generator is a crucial factor for the power generation and therefore for the productivity of the biofuel powerplant. With the implemented solution for the impeller, a steady input pressure is achieved.